Computer models, or simulators, are widely used in a range of scientific fields to aid understanding
of the processes involved and make predictions. Such simulators are often computationally
demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation,
or surrogate, for the simulators accounting for the additional approximation uncertainty.
This thesis develops a novel sequential screening method to reduce the set of simulator
variables considered during emulation. This screening method is shown to require fewer simulator
evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies
subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion,
and thus variance, is typically a function of the inputs. This work extends the emulator framework
to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process
representations and proposes an experimental design technique to optimally learn the model parameters.
The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators,
the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.
|Date of Award||2010|
|Supervisor||Dan Cornford (Supervisor)|
- Gaussian process
- Fisher information
- optimal design
- input-dependent variance